Nonlinear Observers for Systems with State Delay and Randomly Missing Measurements

We present a nonlinear observer for continuous time dynamic system with state delay, and randomly missing measurements. Using the Lyapunov energy (LE) functional, we derive sufficient conditions for the local asymptotic stability for the observer state error equations. The observer performance without and with missing measurements is evaluated by simulations implemented in MATLAB. The results validate the theoretical asymptotic behaviour of the proposed nonlinear observer for the system with time delay and randomly missing measurements. We, then extend the nonlinear observer for nonlinear system with state delay and randomly missing measurements in the measurement data level and state vector fusion modes for multisensory data fusion situation. We also, ascertain that the state vector fusion formula for these observers is similar to that for the Kalman/extended Kalman filter. We ascertain that the derived theoretical result automatically extends to these nonlinear observers due to their non-complicated structures.